Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor x Quotient + Rem. 5x^5 + 4x^4 – 3x^3 + 2x + 2 ;

Question

Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor x Quotient + Remainder’.

5x⁵ + 4x⁴ – 3x³ + 2x² + 2 ; x² – x

Answer 1

5x⁵ + 4x⁴ – 3x³ + 2x² + 2 = 5x⁵ + 4x⁴ – 3x³ + 2x + 0x + 2

∴ Quotient = 5x³ + 9x² + 6x + 8,

 Remainder = 8x + 2 

Now, Dividend = Divisor x Quotient + Remainder 

∴ 5x⁵ + 4x⁴– 3x³+ 2x² + 2 = (x² – x)(5x³ + 9x²+ 6x + 8) + (8x + 2)